Question

Using the remainder theorem, factorise 4x3 + 7x2 – 36x - 63​

Answer 1

Answer:

(x + 3)(4x + 7)(x - 3)

Step-by-step explanation:

p(x) = 4x³ + 7x² - 36x - 63

p(3) = 4(27) + 7(9) - 36(3) - 63 = 0 ⇒ (x - 3) is factor of given polynomial.

(4x³ + 7x² - 36x - 63) ÷ (x - 3) = 4x² + 19x + 21

q(x) = 4x² + 19x + 21

q(- 3) = 4(9) - 57 +21 = 0 ⇒ (x + 3) is factor of (4x² + 19x + 21)

(4x² + 19x + 21) ÷ (x + 3) = 4x + 7

r(x) = 4x + 7

r($-\frac{7}{4}$) = 4($-\frac{7}{4}$) + 7 = 0 ⇒ (x + $\frac{7}{4}$) is factor of (4x + 7)

(4x + 7) ÷ (x + $\frac{7}{4}$ ) = 4

4x³ + 7x² - 36x - 63 = (x + 3)(4x + 7)(x - 3)